Abstract
We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Delta S=1 and Delta S=2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.
Highlights
The renormalisation of four-fermion operators is an essential ingredient in lattice QCD computations of weak matrix elements
In this work we have laid out a general strategy for the non-perturbative renormalisation of operators with Neuberger fermions, via a matching to results obtained with Wilson-type regularisations
We have dealt with the overall logarithmic renormalisation of the operators entering the ∆S = 1 effective Hamiltonian with an active charm quark, for which we have computed renormalisation group invariant (RGI) renormalisation factors in the quenched approximation
Summary
The renormalisation of four-fermion operators is an essential ingredient in lattice QCD computations of weak matrix elements. Our strategy to renormalise Q±1 is similar to the technique proposed in [2] for the computation of the renormalised chiral condensate It involves matching bare correlation functions (or matrix elements) computed with Neuberger fermions to their renormalisation group invariant (RGI) counterparts. The latter are computed in the continuum limit with some variant of Wilson fermions, for which mature techniques for fully non-perturbative renormalisation exist.
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